The Compulsive Gambler Process

Abstract : In the compulsive gambler process there is a finite set of agents who meet pairwise at random times ($i$ and $j$ meet at times of a rate-$\nu_{ij}$ Poisson process) and, upon meeting, play an instantaneous fair game in which one wins the other's money. We introduce this process and describe some of its basic properties. Some properties are rather obvious (martingale structure; comparison with Kingman coalescent) while others are more subtle (an "exchangeable over the money elements" property, and a construction reminiscent of the Donnelly-Kurtz look-down construction). Several directions for possible future research are described. One -- where agents meet neighbors in a sparse graph -- is studied here, and another -- a continuous-space extension called the {\em metric coalescent} -- is studied in Lanoue (2014).
Type de document :
Pré-publication, Document de travail
2014
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https://hal.archives-ouvertes.fr/hal-01003097
Contributeur : Justin Salez <>
Soumis le : lundi 9 juin 2014 - 19:43:54
Dernière modification le : lundi 29 mai 2017 - 14:23:22

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  • HAL Id : hal-01003097, version 1
  • ARXIV : 1406.1214

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INSMI | UPMC | PMA | USPC

Citation

David Aldous, Daniel Lanoue, Justin Salez. The Compulsive Gambler Process. 2014. <hal-01003097>

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